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Pré-Publication, Document De Travail Année : 2023

On the Equilibrium Locus of a Parameterized Dynamical System with Independent First Integrals

Résumé

or a family of dynamical systems with k > 0 independent first integrals evolving in a compact region of Euclidean space, we study the equilibrium locus. We show that under mild and generic conditions, it is a smooth manifold that can be viewed as the total space of a certain fiber bundle and that this bundle comes equipped with a natural connection. We then proceed to show that parallel transport for this connection does exist and explore some of its properties. In particular we elucidate how one can to some extent measure the variation of the eigenvalues of the system restricted to a given the fiber.
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Dates et versions

hal-04259800 , version 1 (26-10-2023)
hal-04259800 , version 2 (18-01-2024)

Identifiants

  • HAL Id : hal-04259800 , version 2

Citer

Yirmeyahu Kaminski, Pierre Lochak. On the Equilibrium Locus of a Parameterized Dynamical System with Independent First Integrals. 2024. ⟨hal-04259800v2⟩
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